The Cardinals have one of the best teams in the game. Shortstop is the one spot where they could seem to use an upgrade, with Pete Kozma holding down the position since Rafael Furcal was lost in spring training.
The White Sox are definite sellers, and Ramirez seems to be the one true shortstop available on the trade market.
The two teams have talked, not just about Ramirez but about Jake Peavy, as well. And one of the White Sox's top scouts was in St. Louis just this week.
Still, an official familiar with the talks responded with "not likely" when asked Saturday if Ramirez could end up in St. Louis.
The White Sox could still be active in the days leading up to the July 31 non-waiver deadline. The Rangers remain interested in Alex Rios, with the Pirates possibly involved, too. The Red Sox appear to be the team most interested in Jake Peavy, but the A's, Braves and Cardinals are also showing interest.
The White Sox are also hoping to sell teams on Matt Lindstrom, but he didn't help them when he gave up three straight hits Friday night against the Royals.